Chicago's tallest building could soon be named after a billionaire's private equity firm

Steve Schwarzman's private equity fund is buying the Willis Tower, it announced Monday. At 110 stories, the Willis Tower bills itself as the fifth-tallest office building in the world (it was first called the Sears Tower).

Blackstone Real Estate Partners VII, a property investment fund that is totally separate from Blackstone's flagship private equity investment vehicles, is making the acquisition, though terms were not made public. However, a report in Crain's had suggested a price tag of $1.5 billion for the deal. On Monday, a report on CNNMoney pegged the purchase price at $1.3 billion.

Blackstone has a recent history of striking big deals for iconic properties. Right before the financial crisis hit, Blackstone did its biggest deal in the form of a $26 billion deal for Hilton Hotels in 2007. Last year, Hilton was brought back onto public markets by Blackstone in a successful IPO, and as the private equity firm has reduced its share in Hilton the hotelier has also struck deals of its own, including the $1.95 billion sale of New York City's Waldorf Astoria hotel to Anbang Insurance Group Co., a Chinese firm.

Blackstone CEO Schwarzman has had a good 2015 so far. His 2014 pay, announced last month at $690 million, far eclipsed his 2013 tally of less than $500 million.

UPDATE: Even though Blackstone is taking possession of the Willis Tower, it will take until 2025 for naming rights to expire.